This preview shows pages 1–6. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: [1] (b) at least one person receives his or her own hat? [1] (c) exactly one person receives his or her own hat? [1] 3 3. (a) Find a closed form (a.k.a. compact form) of the generating function for the sequence a = 0 and a k = (2) k1 , k 1 (i.e., 0 , 1 ,2 , 4 ,8 , 16 ,32 , 64 , . . . ) [3] (b) Find the sequence represented by the generating function f ( x ) = x 2 / (1 + x ) 3 . [3] 4 4. Find the generating function for the sequence a n , n 0, where a n is the number of partitions of n into summands such that (a) each summand is an even number; [2] (b) each summand occurs an odd number of times. [2] 5 5. Find the generating function in a closed form which generates the sequence dened by the following recurrence relation (you do not need to solve for it). a n +12 a n = 5 , n 0; a = 1 . [5]End...
View
Full
Document
This note was uploaded on 01/15/2012 for the course MATH 222 taught by Professor Huangjing during the Spring '11 term at University of Victoria.
 Spring '11
 HuangJing
 Math

Click to edit the document details